Mechanical Hamiltonization of Unreduced ϕ$\phi$‐Simple Chaplygin Systems
ABSTRACT In this paper, we prove that the trajectories of unreduced ‐simple Chaplygin kinetic systems are reparameterizations of horizontal geodesics with respect to a modified Riemannian metric. Furthermore, our proof is constructive and these Riemannian metrics, which are not unique, are obtained explicitly in interesting examples. We also extend these results to ‐simple Chaplygin mechanical systems (not necessarily kinetic).
Authors
- Alexandre Anahory Simoes (ORCID: https://orcid.org/0000-0003-4644-876X)
- Juan Carlos Marrero (ORCID: https://orcid.org/0000-0003-3341-515X)
- David Martı́n de Diego (ORCID: https://orcid.org/0000-0001-6762-8909)
Institutions
- IE University (ES)
- Universidad de La Laguna (ES)
- Institute of Mathematical Sciences (ES)
- Universidad Carlos III de Madrid (ES)
- Universidad Autónoma de Madrid (ES)
Publication Details
- Journal
- Studies in Applied Mathematics
- Published
- 2025-05-01
- DOI
- https://doi.org/10.1111/sapm.70065
- Primary Topic
- Control and Dynamics of Mobile Robots
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Ministerio de Ciencia e Innovación